For each of the statements below, the corresponding activity will lead you to explore a proof by induction of the statement.

- Divisibility
proof 1. For the sequence a
_{n}= a_{n-1}+ 2*n*with a_{1}= 1, a_{n}is always odd. - Divisibility
proof 2. For the sequence a
_{n}= 5a_{n-1}+ 4 with a_{1}= 3, a_{n}is always of the form 4*K*+ 3. - Divisibility
proof 3. For the sequence a
_{n}= 2a_{n-1}+ a_{n-2}with a_{1}= 1 and a_{2}= 2, the sum*n*+ a_{n}is always even. - Divisibility
proof 4. For value of
*n*^{2}+*n*is always even.